The \(|\mathcal {T}^{BH}|^2\)  term is given in [1]},
Eq. (25), and only its general form is reproduced here:
\(|\mathcal {T}^{BH}|^2 =\frac{e^6}{x_B^2 t y^2 (1+\epsilon ^2)^2 \mathcal {P}_1(\phi _{\gamma \gamma }) \mathcal {P}_2(\phi _{\gamma \gamma })}\\\sum _{n=0}^2 c_n^{BH} \cos (n\phi _{\gamma \gamma })\,.\) 
